Mission Possible - 5 Scenarios in 5 Days: Day #4

Objective

SWBAT create equations and inequalities to solve problems.
SWBAT represent relationships between quantitates and constraints graphically.
SWBAT interpret solutions as viable or non-viable options through the context of the mathematical model.

Big Idea

Students will work in small teams to solve a real world problem and present their findings in a whole-class business meeting!

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.*

Cross-Problem Questioning

15 minutes

As the students enter the classroom, I have posted on the board specific seating assignments that correspond to various areas of the classroom. When constructing these groups, I have ensured that they are made up of no more than one representative per problem type (of the 5 problems initially rolled out).

Once the students have all arrived and settle in, I instruct them to take out what they have worked on to this point in the problem and listen for further instructions. This activity is designed to give students a sneak peak into the problems of others, in a way that hopefully helps them in their understanding of the problem that they are working on.

To get the activity started and ensure that we stay together, I pose the following questions for the class to respond in their groups:

1) What are you trying to maximize or minimize in your problem?

2) What are the constraints that you are dealing with?

3) How have you defined your variables?

4) Where are you at in terms of putting your constraints into mathematical form and/or displaying them graphically?

Copy of The 5 Different Entry Documents!.pdf

Work Time Towards Checkpoint

25 minutes

Online Timer

Optional Workshop Request Forms

To close out the class period, I circulate the optional workshop request form. This request is an anonymous way for the students to ask for help with an element of the problem that they do not understand. It is important when solving complex problems with your students that you provide them with every opportunity to get assistance. Although some students do no jump at the first opportunity, most kids will reach out for help if “knocks on the door” enough. Even if the form prompts just one student to ask a question who otherwise would not have, then it is a huge victory!

Prior to dismissing the class, I talk briefly with them about my observations of their work. If things are going well, I inform them that I am not assigning any out of class homework during the activity because I want them to be totally consumed by the problem solving process. However, as a teacher I must be careful that I NEVER insinuate that homework is “punishment” for sub par performance or behavior. Homework is a valuable learning task that sometimes gets plastered by this unhealthy label - - and its no wonder students hate it! I try to be very careful how I word things with my students. Beginning tomorrow, I tell them, they will likely be required to take elements of the project home to begin to tie it all together for their final business meeting presentation.